source parameters of the skyros island (north aegean sea)...

ANNALS OF GEOPHYSICS, VOL. 45, N. 3/4, June/August 2002

513

Source parameters of the M 6.5Skyros Island (North Aegean Sea)

earthquake of July 26, 2001

Christoforos Benetatos (1), Zafeiria Roumelioti (1), Anastasia Kiratzi (1)and Nikos Melis (2)

(1) Department of Geophysics, Aristotle University of Thessaloniki, Greece(2) Institute of Geodynamics, National Observatory of Athens, Greece

AbstractTeleseismic body wave modelling, time domain moment tensor inversion of regional waveforms and spectralanalysis of the far-field P-wave pulses are used to derive the source parameters of the July 26, 2001 Skyrosearthquake (M 6.5). Its epicentre is located south of the Sporades Islands in the North Aegean Sea (Greece).Previous focal mechanism solutions indicate motion on strike-slip faults. The time domain moment tensor inversionis applied for the first time to the regional waveforms of the recently established broadband network in Greece. Itsapplication gave results which are highly consistent with teleseismic waveform modelling. The results of thisstudy, in combination with the distribution of aftershocks, indicate left-lateral strike slip motion on a NW-SEstriking fault with parameters: fault plane (strike = 151°, dip = 83°, rake = 7°) and auxiliary plane (strike = 60°,dip = 84°, rake = 173°), depth 12 km and M0 = 5.98e18 N m. Moreover, the time domain moment tensor inversiontechnique yielded a pure double couple source with negligible CLVD. The spectral analysis of the far-fieldP-wave pulses resulted in a fault length L ~ 32 km, stress drop ~ 9 bars and average displacement u ~ 30 cm.These values are in very good agreement with those estimated from empirical scaling relations applicable to theAegean area.

1. Introduction

On July 26, 2001 an earthquake of M 6.5occurred in the Aegean Sea, a few kilometres NWof the island of Skyros (fig. 1). Despite its largemagnitude and the fact that it was felt in a wideregion, the earthquake did not cause extensivedamage as its epicentre was located at sea

(38.995°N, 24.382°E; Geophysical Laboratory,Aristotle University of Thessaloniki). Limiteddamage was only observed in the island ofSkyros, concerning mainly old residentialbuildings, a 1000-year-old monastery locatedinside the island’s castle and limited landslidesand rock falls.

The aim of this paper is to investigate in de-tail the source parameters of the Skyros main-shock. We use teleseismic data from the GlobalSeismograph Network (GSN) as well as regionalbroadband waveforms recorded by the recentlyinstalled broadband network operated by theNational Observatory of Athens (NOA). Thefocal mechanism and related parameters aredetermined through a comparative application oftwo different methodologies: teleseismicwaveform modelling (Nábelek, 1984) and time

Mailing address: Prof. Anastasia A. Kiratzi, Department ofGeophysics, Aristotle University of Thessaloniki, GR 54124,Thessaloniki, Greece; e-mail: [email protected]

Key words source parameters Skyros earthquakeAegean Greece

514

Christoforos Benetatos, Zafeiria Roumelioti, Anastasia Kiratzi and Nikos Melis

domain moment tensor inversion (Dreger, 2000).The latter methodology is applied for the firsttime in the study of Aegean earthquakes.Furthermore, the dimensions of the causativefault, the stress drop and the average dis-placement across the ruptured area, are de-termined from the far-field displacement spectraof the event.

2. Teleseismic waveform modelling

2.1. Methodology and application

The technique of body-waveform modelling,described in detail by Nábelek (1984) andMcCaffrey et al. (1991), was used to calcu-late the focal mechanism of the Skyros main-

North Aegean Trought

Sporades Isl.

M

Fig. 1. Regional map showing the sites of the broadband stations, operated by the Geodynamic Institute of theNational Observatory of Athens, and the epicentre location (asterisk) of the Skyros July 26, 2001 earthquake.

515

Source parameters of the M 6.5 Skyros Island (North Aegean Sea) earthquake of July 26, 2001

.Fig. 2. Teleseismic waveform modelling results: comparison between observed (solid line) and synthetic (dashedline) P and SH long-period waveforms. The estimated strike, dip and rake (in degrees), the depth (in km) and theseismic moment (in N m) are shown at the top of the figure. Stations are ordered clockwise by azimuth and thestation code of each waveform is accompanied by a letter corresponding to its position within the focal sphere.Vertical bars show the inversion window. The employed source time function and the waveform time scale aredepicted at the centre of the figure. Waveform amplitude scales (in microns) are shown to the left of the focalsphere. The insets show the first motion polarities at stations with epicentral distances lower than 30°, not includedin the inversion, but complimentary used to constrain the nodal planes.

516


shock. The employed data consist of P andSH waveforms from stations of the GlobalSeismograph Network (GSN). All waveformshave a sampling frequency of 1 Hz and wererecorded at epicentral distances ranging from 30°to 90°. The nodal planes of the focal mechanismwere constrained by the use of P-wave polaritiesfrom stations located at distances less than 30°.The applied methodology has been extensivelydescribed in past papers (e.g., Kiratzi and

Louvari, 2001; Louvari and Kiratzi, 2001) andtherefore we will only present a brief descriptionof it.

A FIR (Finite Impulse Response) band passfilter was first applied to the data, in order toremove the high frequency noise. The cornerfrequencies of the filter were determined visually,by comparing the FFT amplitude spectrum ofthe signal with the corresponding spectrum ofthe noise. In most cases, the frequencies of inter-

Table I. Source parameters of the July 26, 2001 Skyros earthquake derived from the two applied methodologies.In the case of the teleseismic waveform modelling, the numbers in the brackets indicate the lower and upperbounds of the uncertainties.

Method Time Lat. Long. M M0×1018 Depth 1st Plane 2nd PlaneH:M:S (°N) (°E) (N m) (km) Strike (°) Dip (°) Rake (°) Strike (°) Dip (°) Rake (°)

Teleseismic 00:21:38 38.99 24.38 6.4 4.46 12 145 80 8 54 82 170waveform modelling (+1/-3) (+5/-2) (+3/-3) (+4/-2)

Time domain moment 00:21:38 38.99 24.38 6.5 5.43 14 156 86 5 66 85 176tensor inversion

Fig. 3. Comparison of the «minimum misfit solution» obtained in this study (upper part) to the Harvard CMTsolution (lower part). The solutions are not very different but our solution gives a considerably better fitting (HIAand AAK for instance).

517


Fig. 4. Presentation of the tests performed in order to define the uncertainties in strike, dip, rake and depth (asdiscussed in the text and listed in table I).

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est in the Long-Period waveforms covered therange from f1 = 0.01 Hz to f2 = 0.1 Hz. Theaforementioned frequency limits were used ascorner frequencies of the filter. All waveformswere integrated to displacement prior to theinversion.

We used the MT5 version of McCaffrey andAmbers (1988) algorithm to invert P and SHwaveform data in order to obtain the strike, dip,rake, centroid depth, seismic moment and sourcetime function of the examined event. Themethodology assumes that the source can berepresented as a point (the centroid) in space,although not in time. The time history of thedisplacement on the fault is represented by asource time function made up of a series ofoverlapping isosceles triangles, whose numberand duration are defined by the user. Theinversion routine yields amplitudes for eachtriangular shape. Amplitudes were corrected forthe geometrical spreading, the epicentral distance(Langston and Helmberger, 1975), and theattenuation using Futterman’s (1962) operatorwith t* = 1 s for P- and t* = 4 s for SH-waves.The inversion adjusts the relative amplitudes ofthe source time function elements, the centroiddepth, the seismic moment and the sourceorientation (strike, dip, rake) to minimize themisfit between observed and syntheticseismograms. We refer to this solution as the«minimum misfit solution». The covariancematrix associated with the «minimum misfitsolution» usually underestimates the true un-certainties associated with the source para-meters. To find more realistic uncertainties, wefollowed the methodology of McCaffrey andNábelek (1987) and Molnar and Lyon-Caen(1989) by fixing some of the source parametersat values close to, but different from those ofthe «minimum misfit solution» and allowing allthe other parameters to vary during the in-version. The errors are determined by visualexamination when the match of the observedto synthetic seismograms significantly dete-riorates.

Synthetics were generated for a point sourceburied in a half-space. We used a P-wave velocityof 6.5 km/s, S-wave velocity 3.7 km/s and density2.75 g/cm3. We also used a 300 m water layeroverlying the half-space.

2.2. Inversion results

The focal mechanism of the 26 July 2001earthquake was computed by inverting 24 P -and 22 SH - Long-Period waves with goodazimuthal coverage (fig. 2). The results areshown in table I. First-motion polarities ofP- waves recorded at 8 stations located at epi-central distances 0°-30° are compatible withthe inversion solution. The inversion yieldeda source time function of boxcar shape andduration of ~ 8 s. Our solution is in good agree-ment with the solution published in theHarvard CMT catalogue, although the syn-thetics produced by the CMT solution (strike,dip and rake fixed, all other parameters free)indicate poor amplitude fitting for somestations like HIA, AAK and KDAK as shownin fig. 3.

Figure 4 summarizes some of the tests thatwere carried out, in order to investigate theerrors of our minimum misfit solution. Thefixed values for strike, dip, rake and depth testsare 135° and 170°, 70° and 90°, 20° and 0° and16 km and 7 km, respectively.

3. Time domain moment tensor inversion

3.1. Methodology

In addition to the teleseismic waveformmodelling, we applied the time domainmoment tensor inversion technique, which usesdigital waveform data recorded at regionaldistances. The employed inversion code hasthe capability of revealing the seismic momenttensor using a single three-component station,although the use of a larger number of stationsprovides greater stability (Dreger and Helm-berger, 1991). Generally, the methodology canbe applied successfully if the following con-ditions are met: 1) the regional crustal modelis sufficiently well known to explain the low-frequency part of the recorded waveforms; 2)the event location can be well represented bythe high-frequency hypocentral location, and3) the source time history is synchronous forall of the moment tensor elements and may beapproximated by a delta function (Dreger,

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2000). Furthermore, the inversion procedureaccounts only for the deviatoric tensor, neg-lecting any volumetric changes in the source area.

The applied methodology is based on asimplified general representation of the seismicsource by considering a point source in bothspace and time

(3.1)

where Un is the nth observed component ofdisplacement, Gni,j is the nth component of thetheoretical Green’s function for specific force-couple orientations, x corresponds to the source-station distance, z is the source depth and Mij isthe scalar seismic moment tensor. The generalforce-couples for the deviatoric moment tensorare represented by the three fundamental faults,namely a vertical strike-slip, a vertical dip-slipand a 45° dip-slip (Jost and Herrmann, 1989).

Equation (3.1) is solved using linear leastsquares, assuming a constant source depth foreach inversion. The estimated scalar seismicmoment tensor, Mij, is then decomposed into thescalar seismic moment, a double-couple momenttensor and a compensated linear vector dipolemoment tensor. The procedure of the de-composition is described in detail in Jost andHerrmann (1989). The optimum hypocentraldepth is found iteratively through an examinationof both an objective function and the variancereduction. The objective function, f, dependsupon the RMS of the difference between theobserved waveforms (d ) and the syntheticwaveforms (s), modulated by the percent doublecouple ( pdc):

(3.2)

while the Variance Reduction (VR), is estimatedthrough the relation

(3.3)

U x t M G x z tn ij ni j, , ,,( ) = ( )

fd s

=( )RMS

pdc

Successful applications of the methodology resultin small values of the objective function and largevalues of the variance reduction, indicating thatboth the waveform fit and the percent doublecouple are large.

3.2. Application and inversion results

In order to apply the time domain momenttensor inversion technique for estimation ofthe Skyros mainshock focal mechanism, anappropriate 1D velocity model had to be cho-sen. Unfortunately, due to the geological andseismotectonic complexity of the Aegean area,one single 1D model is not adequate to explainthe low-frequency wave propagation alongthe different wave paths (see fig. 1 and http://www.gein.noa.gr for more information on theNOA stations). Recently, Zahradnik (2001)tested the model proposed by Novotny et al.(2001), through a forward simulation of thesame waveforms used in the present study(regional broadband data of NOA) and foundthat the examined 1D model can satisfactorilyexplain the frequency range 0.05-0.08 Hz ofthe waveforms recorded at stations APE, PRKand ATH (fig. 1). These stations are amongthe closest to the mainshock epicentre (theirepicentral distances range from 135 to 245 km)and present the larger signal to noise ratios.

We also employed the model of Novotnyet al. (2001) and used it as input in the frequency-wavenumber integration code (FKRPROG)developed by Saikia (1994) in order to computesynthetic Green’s functions for the examinedepicentre-station distances. The synthetic Green’sfunctions were then used in the time domainmoment tensor inversion code to derive the focalmechanism of the examined event.

We found that the employed velocity modelworks very well for stations ATH, PRK andAPE (variance reduction is larger than 90% forall three stations), although it is inadequate forthe rest of the epicentre-station paths. Never-theless, the applied methodology gives reliableresults by using one single station, thus thecombination of three stations provides highlevels of accuracy in the derived focal mech-anism.

VRd s dt

d dt=

[ ]1 0

2

. .2

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The results from the time domain momenttensor technique are presented in fig. 5 andtable I. The observed tangential, radial andvertical components at stations APE, PRK andATH (solid lines) are compared to the synthetics(dashed lines). Table I shows that the two appliedmethodologies gave converging results.

4. Source parameters from far-fielddisplacement spectra

4.1. Methodology

Source parameters such as moment (M0), faultlength (L), average displacement (u

_) across the

fault and static stress drop ( ), were determinedfor the Skyros mainshock, using the far-field

amplitude displacement spectra. The data consistof Long Period P-waves (sampling frequency1 Hz) recorded at teleseismic distances (30°-90°)from the GSN stations. We used a time windowstarting at the P-arrival and ending before theS-wave arrival. The displacement waveformswere corrected for the instrument response,attenuation and radiation pattern. For the lattercorrection we used an average radiation patternover the focal sphere, which in the case of the P-waves is assigned the value R = 0.51 (Fletcher,1980). The far-field amplitude displacementspectra are characterized by 3 parameters: i) thelow frequency level 0, which is proportionalto seismic moment; ii) the corner frequency, fc,and iii) the power of the high frequencyasymptote. Following Brune (1970, 1971), weshall define corner frequency at the intersection

Fig. 5. Results of the time domain moment tensor inversion. In the left part the comparison between observed(solid line) and synthetic (dashed line) regional broadband waveforms is shown. In the right part the beach-ball,of strike, dip and rake for the two nodal planes, the scalar seismic moment, M0, and the moment magnitude,M are also given. The time scale is shown below the vertical component, while information on the station name,examined frequency range, maximum observed amplitude (in cm) and variance reduction is shown below wave-forms.

TANGENTIAL RADIAL VERTICAL

30.00s

30.00s

30.00s

Strike = 156; 66Rake = 5; 176Dip = 86; 85Mo = 5.43e+25

= 6.5Percent DC = 99Percent CLVD = 1

M

Station: ATH Frequency_interval: 0.05-0.08 Hz Max_ampl= 2.92e-01cm VR=91.7%

Station:PRK Frequency_interval: 0.05-0.08 Hz Max_ampl= 4.03e-01cm VR=94.3%

Station:APE Frequency_interval: 0.05-0.08 Hz Max_ampl= 4.53e-01cm VR=92.0%

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0.01 0.1

1E-6

1E-5

1E-4

= 1.7 E-04

fc

= 0.07Am

plitu

de

(m*s

)

Frequency (Hz)

BRVK

0.01 0.1

1E-6

1E-5

1E-4

1E-3

= 1.92 E-04

fc

=0.069Am

plitu

de

(m*s

)

Frequency (Hz )

CMLA

1E-3 0.01 0.1

1E-7

1E-6

1E-5

1E-4

= 7.24 E-05

fc

= 0.067Am

plitu

de

( m*s

)

Frequency (Hz)

DWPF

1E-3 0.01 0.1

1E-7

1E-6

1E-5

1E-4

= 9.03 E-05

fc

= 0.065Am

plitu

de

(m*s

)

Frequency (Hz)

HRV

0.01 0.1

1E-7

1E-6

1E-5

1E-4

= 9.93 E-05

fc

= 0.064Am

plitu

de

(m*s

)

Frequency (Hz)

SFJ

0.01 0.1

1E-7

1E-6

1E-5

1E-4

1E-3

= 1.14 E-04

fc

= 0.077Am

plitu

de

(m*s

)

Frequency (Hz )

TLY

0

0

0

0

0

0

Fig. 6. Far-field amplitude displacement spectra used to estimate the fault dimensions and other parameters ofthe Skyros mainshock. The low and high frequency asymptotes (fitted by eye) are depicted as straight lines. Thecorresponding values of the low-frequency part of the spectrum, 0, and the corner frequency, fc, are also shownfor each spectrum.

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of low- and high-frequency asymptotes in thespectrum.

Almost all far-field displacement spectrawere characterized by a constant low-frequencylevel, 0, and a fall-off above a corner frequencyfc, at a rate proportional to f y. Spectra that didnot show such a shape were not analysed.Determination of the spectral parameters ( 0,fc) was performed be eye fitting low- and high-frequency asymptotes to the observed spectra.Figure 6 shows indicatively the displacementamplitude spectra for 6 stations together withtheir best fitting results.

The scalar seismic moment was calculatedfrom the relation (Keilis-Borok, 1959)

(4.1)

where 0(P) denotes the low-frequencyasymptote of the spectrum, the density, Rthe radiation pattern coefficient for P-wavesfrom a double couple point source, R the epi-central distance and the P-wave velocity atthe source.

In order to calculate the source dimensionsand the stress drop, a circular fault of radius rwas assumed. Following Madariaga (1976), theradius of the source can be estimated fromrelation

(4.2)

where fcp is the corner frequency of the P-wavespectra and is the velocity of the S-waves. Wehave also assumed that the diameter of thecircular fault area is equal to the observed faultlength (Hanks and Wyss, 1972).

Stress drop was calculated from the relationof Keilis-Borok (1959)

(4.3)

and the average displacement, u, was calculated

from the relation of Aki (1966)

(4.4)

where µ is the shear modulus (taken equal to3.3*1010 N/m2) and A is the fault surface in km2.

Average values <x> were computed for eachparameter (stress drop, fault length, averagedisplacement) following Archuleta et al. (1982):

(4.5)

where N is the number of stations used. Thebasic reason for using this relation is that in thecase of simple arithmetic average, the meanvalues are biased towards the larger values. Thecorresponding standard deviation of thelogarithm SD(log<x>) and the multiplicativeerror factor, Ex, were also calculated from therelations of Archuleta et al. (1982):

(4.6)

(4.7)

4.2. Source parameters of the mainshock fromthe spectral analysis

The distance, azimuth, the radiation patternof the P-waves, R (P), the low frequencyasymptote, 0, and the corner frequency, fc, ofthe stations used are listed in table II. Table IIIlists the average values and the multiplicativeerror factor of the stress drop, the radius of thecircular fault and the average displacementacross the ruptured area. In our calculations,we used 6.5 km/s for the P-wave velocity, 3.7km/s for the S-wave velocity, 2.6 g/cm3 fordensity and 3.3*1010 Nt/m2 for the shear mo-dulus, µ.

M PP

R PR0

0 34( ) =( )( )

=7

16

0

3

M

r

M Au0 = µ

< > ==

xN

xi

i

N

anti log ( )1

1

log

SD log log log< >( ) = < >( )=

xN

x xi

i

N1

1

2

1

1

2

E SD xx = < >( )( )anti log log .

r Pfcp

( ) =0 32.

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Station Epicentral Azimuth Take-off angle Omega Corner frequencycode distance (°) (°) (m.s) (Hz)

(km)

MA2 5232 27 21 1.45E-04 0.064

MAJO 7241 48 18 1.02E-04 0.071

TLY 4233 49 27 1.14E-04 0.077

BRVK 2618 50 32 1.70E-04 0.070

BJT 5734 56 23 1.13E-04 0.070

WMQ 3855 63 29 1.47E-05 0.075

MDJ 6006 64 21 9.00E-05 0.071

XAN 5802 65 23 1.85E-04 0.074

CHM 3130 67 31 1.59E-04 0.080

TKM2 3184 67 31 1.46E-04 0.083

USP 3104 67 31 1.23E-04 0.092

ENH 6147 68 24 1.30E-04 0.072

AAK 3128 68 31 1.59E-04 0.087

EKS2 3084 68 31 1.86E-04 0.081

KBK 3155 68 31 1.82E-04 0.079

ULHL 3250 68 31 1.63E-04 0.069

UCH 3146 69 31 1.67E-04 0.079

AML 3099 69 31 1.59E-04 0.081

CHTO 6356 85 23 1.35E-04 0.065

MSEY 5370 140 28 1.02E-04 0.089

BOSA 7196 180 23 1.18E-04 0.078

ASCN 6167 227 25 1.05E-04 0.088

BDFB 9182 247 17 5.29E-05 0.075

SACV 4737 254 28 1.24E-04 0.070

SJG 7648 285 19 8.16E-05 0.070

CMLA 3382 285 31 1.92E-04 0.069

DWPF 7715 302 18 7.24E-05 0.067

HRV 5786 308 22 9.03E-05 0.065

WVT 7245 311 18 6.21E-05 0.075

BORG 2545 329 31 1.00E-04 0.087

SFJ 3292 330 28 9.93E-05 0.064

COLA 5232 357 20 9.73E-05 0.063

Table II. Station parameters and spectral parameters obtained from the far-field displacement spectra ofP-waves for the July 26, 2001 Skyros earthquake.

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Table III. Mean values and multiplicative error factors of the seismic moment, M0, the fault radius, r, the stressdrop, and the average displacement, u, as defined by means of the far-field P-wave spectral analysis.

M0 r (km) (bars) u (cm)(1018 N m)

Mean value 8.06 15.9 8.7 31

Multiplicative error 1.94 1.11 1.97 1.92

Standard deviation ± 5.34 ± 1.7 ± 5.9 ± 20.0

Fig. 7. Regional map showing the focal mechanism of the Skyros mainshock, the distribution of the aftershocks,the orientation of the fault that moved during the earthquake, and other focal mechanisms previously determined.The activation of an NW-SE striking fault is evident.

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The scalar moment, based on eq. (4.1), isM0= 8.06.1018 N m. This value is larger comparedto the values obtained by the teleseismic bodywaveform modelling and the time domainmoment tensor inversion. Nevertheless, thepreviously determined values for the seismicmoment of the examined event lie within therange of ± 1 standard deviation of the presentestimation from the spectral analysis.

5. Conclusions

We investigated the source parameters ofthe Skyros M 6.5 earthquake that occurred in theNorthern Aegean Sea using body wave tele-seismic waveform modelling, time domainmoment tensor inversion using regional wa-veforms, as well as spectral analysis of the far-field displacement P-wave spectra. We used thefirst two methodologies, in parallel, both toensure reliable estimation of the focal mech-anism, for further use in more detailed studies ofthe source process during the Skyros event (e.g.,slip distribution studies), and to validate theresults of the time domain moment tensorinversion, which is applied for the first time inthe Aegean area. The converging results of bothmethodologies were quite encouraging forfurther application of the time domain momenttensor inversion scheme to study moderate sizeAegean earthquakes.

The parameters of the July 26, 2001 Skyrosearthquake, averaging the values obtained, are:fault plane (strike = 151°, dip = 83°, rake = 7°)and auxiliary plane (strike = 60°, dip = 84°, rake= 173°), depth 12 km and M0 = 5.98e18 N.m,fault length L ~ 32 km, stress drop ~ 9 barsand average displacement u ~ 30 cm.

Figure 7 shows the focal mechanism of themainshock together with previously determinedfocal mechanisms of earthquakes of the area(Papazachos et al., 1998 and references therein).In the same figure, the aftershock distribution isalso shown for comparison (Melis et al., 2001).It is seen that the NW-SE striking plane is thefault plane which implies sinistral strike-slipmotion contrary to what is expected from thestrands of the North Anatolian Fault zone thatterminates in this area, which is well known for

its dextral strike-slip character. This observationof sinistral strike-slip motion in the NorthernAegean Sea is documented for the first time fromthe study of an earthquake recorded by themodern global and regional networks. Thesignificance of the NW-SE striking structures,inherited from the old compressional phase ofthe Aegean tectonics will be further discussed inanother paper. However, this event gave strongevidence that these structures can be activatedfrom the modern stress field presently acting inthe Aegean area.

Acknowledgements

Green’s functions were computed using theFKRPROG software developed by ChandanSaikia with URS Granger, Woodward ClydeFederal Services. The time domain momenttensor inversion was based on the code developedby Douglas Dreger of the Berkeley SeismologicalLaboratory, and kindly provided to us. This workwas partially supported by the EarthquakePlanning and Protection Organisation (OASP) ofGreece through project 20246/2000 and byProjects 972342 (Seis - Albania) and 1868/99GSRT.

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(received February 21, 2002;accepted May 27, 2002)

source parameters of the skyros island (north aegean sea)...

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